Consider one particular source. Suppose the freshest update at the monitor at time \(t\)  is generated at time \(u(t)\) , the age of information at the monitor (in short, AoI) is defined as \(\Delta (t) =t-u(t)\) , which is the time elapsed since the generation of the last received update [1]}.
From the definition, it is clear that AoI linearly increases at a unit rate with respect to \(t\) , except some reset jumps to a lower value at points when the monitor receives a fresher update from the source. The age of information of our network is shown in Figure REF .
For a particular source, let \(t_{1}, t_{2},\dots , t_N\)  be the generation times of all transmitted updates at all servers in increasing order.
The black dashed lines show the age of every update.
Let \(T_{1}, T_{2},\dots , T_N\)  be the receipt time of all updates. Note that due to the contention among different updates at the same server, some updates may be dropped and not delivered at all. The red solid lines show AoI.
